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Open AccessArticle

Entropy Production in Exactly Solvable Systems

1
Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK
2
Centre for Complexity Science, Imperial College London, London SW7 2AZ, UK
3
The Francis Crick Institute, 1 Midland Rd, London NW1 1AT, UK
4
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
5
Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, UK
*
Author to whom correspondence should be addressed.
These authors have contributed equally to this work.
Entropy 2020, 22(11), 1252; https://doi.org/10.3390/e22111252
Received: 8 October 2020 / Revised: 30 October 2020 / Accepted: 1 November 2020 / Published: 3 November 2020
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Stochastic Processes)
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms. View Full-Text
Keywords: entropy production; active matter; exact results; stochastic thermodynamics entropy production; active matter; exact results; stochastic thermodynamics
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MDPI and ACS Style

Cocconi, L.; Garcia-Millan, R.; Zhen, Z.; Buturca, B.; Pruessner, G. Entropy Production in Exactly Solvable Systems. Entropy 2020, 22, 1252. https://doi.org/10.3390/e22111252

AMA Style

Cocconi L, Garcia-Millan R, Zhen Z, Buturca B, Pruessner G. Entropy Production in Exactly Solvable Systems. Entropy. 2020; 22(11):1252. https://doi.org/10.3390/e22111252

Chicago/Turabian Style

Cocconi, Luca; Garcia-Millan, Rosalba; Zhen, Zigan; Buturca, Bianca; Pruessner, Gunnar. 2020. "Entropy Production in Exactly Solvable Systems" Entropy 22, no. 11: 1252. https://doi.org/10.3390/e22111252

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